1. NAME AND TITLE
ETRAN: Monte Carlo Code System for Electron and Photon Through Extended Media.
DATATAPE 2C: Data Library.
DATAPAC 6: Data Processing Code.
ETRAN 16D: One-dimensional Transport Code.
ETRAN 18G: Cylindrical Transport Code.
INCLUDE: FORTRAN V Statements for use with ETRAN 16D and 18G.
ETRAN was originally packaged in 1968; has been updated several times in response to user
feedback and continuing development by the code developers at NBS. It has been widely
distributed (153 times by RSIC, 1968mid 1981) and was featured in an RSIC-sponsored seminar-workshop (58 attendees) in 1968.
Center for Radiation Research, National Bureau of Standards, Washington, D. C.
3. CODING LANGUAGE AND COMPUTER
FORTRAN IV; IBM 360/75/91; compatible with other IBM and UNIVAC computers.
4. NATURE OF PROBLEM SOLVED
ETRAN computes the transport of electrons and photons through plane-parallel slab targets that
have a finite thickness in one dimension and are unbound in the other two dimensions. The incident
radiation can consist of a beam of either electrons or photons with specified spectral and directional
distribution. Options are available by which all orders of the electron-photon cascade can be
included in the calculation. Thus electrons are allowed to give rise to secondary knock-on
electrons, continuous bremsstrahlung and characteristic X-rays; and photons are allowed to produce
photo-electrons, Compton electrons, and electron-positron pairs. Annihilation quanta, fluorescence
radiation, and Auger electrons are also taken into account. If desired, the Monte Carlo histories of
all generations of secondary radiations are followed. The information produced by ETRAN
includes the following items: (1) the reflection and transmission of electrons or photons, differential
in energy and direction; (2) the production of continuous bremsstrahlung and characteristic X-rays
by electrons and the emergence of such radiations from the target (differential in photon energy and
direction); (3) the spectrum of the amounts of energy left behind in a thick target by an incident
electron beam; (4) the deposition of energy and charge by an electron beam as function of the depth
in the target; (5) the flux of electrons, differential in energy, as function of the depth in the target.
5. METHOD OF SOLUTION
A program called DATAPAC 6 takes data for a particular material from a library tape and further processes them. The function of DATAPAC 6 is to produce single-scattering and multiple-scattering data in the form of tabular arrays (again stored on magnetic tape) which facilitate the rapid sampling of electron and photon Monte Carlo histories in ETRAN.
The photon component of the electron-photon cascade is calculated by conventional random sampling that imitates the physical processes of Compton scattering, photoelectric absorption, and pair production. In the calculation of the electron component, no attempt is made to follow successive individual interactions with atoms and atomic electrons because these are too numerous.
Instead, a Monte Carlo model is used in which attention is focused on the effect of groups of successive collisions.
The electron tracks to be sampled are divided into a large number of short segments, and the energy loss and angular deflection in each segment are sampled from pertinent theoretical multiple scattering distributions. At the end of each short step, the direction of motion of the electron is changed by a multiple scattering angular deflection that is sampled from the Goudsmit-Saunderson distribution. This distribution is assumed to be the same for all short steps lying within a given step. The energy loss in a step, resulting from the cumulative effect of many inelastic collisions, is sampled from a distribution that is a convolution of a Landau distribution with a Gaussian. An option is also provided for using the continuous-slowing-down approximation in which energy-loss fluctuations are disregarded and the energy loss by collisions is simply computed with the use of the stopping power formula. The production of knock-on electrons is sampled in each short step with the use of a probability distribution derived from the Moller cross section for collisions between free electrons (binding effects are disregarded). Histories of these particles are then followed by procedures identical with those used for the primary electrons.
The production of continuous bremsstrahlung photons is sampled in each short step with the use of a probability distribution derived from the bremsstrahlung cross section (Bethe-Heitler theory with modifications taking into account the correct high-frequency limit, empirical corrections, etc.). The probability is usually quite small that more than one bremsstrahlung photon will be produced in a single short step. Allowance is made for such a contingency by sampling the frequency of bremsstrahlung production events from a Poisson distribution. The energy of the secondary bremsstrahlung photons is subtracted from the energy of the electrons producing them. Thus photon emission contributes to the energy-loss straggling of the electrons. The photons are started out at a random position in the short step in a direction relative to that of the primary electron specified by the sampled intrinsic bremsstrahlung emission angle. For problems in which the production of thick-target bremsstrahlung is of prime interest, there is an option to increase the rate of occurrence of bremsstrahlung events artificially by a specified factor.
The production of secondary characteristic X-rays in each short step is sampled with the use of the K-ionization cross sections of Arthurs and Moiseiwitsch and Kolbenstvedt. The program is arranged so as to treat simultaneously many slab targets with different thicknesses. Boundary crossings (transmission and reflection) usually occur in the middle of a short step. The energy with which the electron crosses the border is determined by subtracting from the energy at the beginning of the step an energy loss sampled from the Landau-Blunck-Leisegang distribution for the fraction of the step taken to the boundary. The direction at the time of crossing is determined by changing the direction of motion at the beginning of the short step involved, using a deflection sampled from an exponential approximation to the Goudsmit-Saunderson distribution for the fraction of the short step to the boundary.
The target is subdivided into many thin sublayers of equal thickness, and the energy deposited
in each sublayer is recorded for each sampled track. The energy allowed to be deposited is that
dissipated by electrons in inelastic collisions resulting in the production of slow secondary electrons
with energies below the chosen cut-off value. The energy given to fast secondary electrons with
energies above the cut-off is not immediately scored, because the histories of these electrons are
followed further so that the energy may eventually be deposited in a sublayer different from the one
in which the electrons were produced. Bremsstrahlung losses are similarly not scored immediately.
Photons are allowed first to penetrate further through the medium so that the energy of the
electrons set in motion by them may eventually be deposited in a different sublayer. The treatment
of charge deposition is quite similar to that of energy deposition, involving the scoring of charge
deposited in sublayers. A track is assumed to "end" when the residual range of the electron is so
small compared to the size of the sublayers that escape to a different sublayer is no longer possible.
When secondary electrons are produced, either as the result of a knock-on collision or as the result
of Compton scattering or photoelectric absorption, a unit charge is withdrawn from the sublayer in
which the electron is born. Electron-positron pairs are excluded from this scheme because on the
average their production does not lead to a net transfer of charge. The electron flux is computed in
ETRAN as a quantity differential in energy but integrated over all directions. A Monte Carlo
estimate of the flux is obtained by dividing the target into many sublayers and scoring the track
length of electrons with specified energies in each of the sublayers. The average track length per
incident electron divided by the thickness of the sublayer provides an estimate of the average flux
in the sublayer. The flux calculation includes primary as well as secondary electrons with energies
down to some cut-off value which is chosen so that the electron is effectively trapped in the
sublayer in which it finds itself, because its residual range is smaller than the distance to the nearest
sublayer boundaries. The flux differential in angle is also computed, and a distinction is made
between the flux in the forward and backward directions.
6. RESTRICTIONS OR LIMITATIONS
No dimensional limitations are noted.
7. TYPICAL RUNNING TIME
No study of typical running time has been made by RSIC.
8. COMPUTER HARDWARE REQUIREMENTS
The code requires the use of a large computer. It is operable on the UNIVAC 1108 and the
IBM 360/370, with standard I-O and two tape units or direct access devices.
9. COMPUTER SOFTWARE REQUIREMENTS
FORTRAN IV operating systems.
M. J. Berger and S. M. Seltzer, "Electron and Photon Transport Programs (Program DATAPAC 4)," NBS-9836 (June 1968).
M. J. Berger and S. M. Seltzer, "Electron and Photon Transport Programs (Program ETRAN 15)," NBS-9837 (June 1968).
M. J. Berger and S. M. Seltzer, Informal Notes on DATAPAC 6, ETRAN 16D, and ETRAN
11. CONTENTS OF CODE PACKAGE
Included are the referenced documents and one (1.2MB) DOS diskette which contains library
data, source for each code and input and output for a sample problem.
12. DATE OF ABSTRACT
May 1969; updated July 1981, February 1985.
KEYWORDS: MONTE CARLO; ELECTRON; SLAB; CYLINDRICAL GEOMETRY; GAMMA-RAY